A: `K_(4)[Fe(CN)_(6)]`is less stable than `K_(3)[Fe(CN)_(6)]`
R: In `K_(4)Fe(CN)_(6)]` the EAN of Fe is 36

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. ) If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the question regarding the stability of the coordination compounds \( K_4[Fe(CN)_6] \) and \( K_3[Fe(CN)_6] \), we will analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion and Reason**:
- The assertion states that \( K_4[Fe(CN)_6] \) is less stable than \( K_3[Fe(CN)_6] \).
- The reason given is that in \( K_4[Fe(CN)_6] \), the Effective Atomic Number (EAN) of iron is 36.

2. **Determine the Oxidation State of Iron in Both Compounds**:
- For \( K_4[Fe(CN)_6] \):
- Let the oxidation state of iron be \( x \).
- The equation can be set up as follows:
\[ 4(1) + x + 6(-1) = 0 \implies 4 + x - 6 = 0 \implies x = +2 \]
- Therefore, the oxidation state of iron in \( K_4[Fe(CN)_6] \) is +2.

- For \( K_3[Fe(CN)_6] \):
- Let the oxidation state of iron be \( y \).
- The equation can be set up as follows:
\[ 3(1) + y + 6(-1) = 0 \implies 3 + y - 6 = 0 \implies y = +3 \]
- Therefore, the oxidation state of iron in \( K_3[Fe(CN)_6] \) is +3.

3. **Stability Consideration**:
- The stability of coordination compounds is influenced by the oxidation state of the metal ion and the nature of the ligands.
- In this case, \( CN^- \) is a strong field ligand, and the higher the oxidation state of the metal ion, the greater the interaction with the ligands.
- Since \( K_3[Fe(CN)_6] \) has iron in the +3 oxidation state, it will have a stronger interaction with the \( CN^- \) ligands compared to \( K_4[Fe(CN)_6] \) where iron is in the +2 oxidation state. This results in \( K_3[Fe(CN)_6] \) being more stable.

4. **Effective Atomic Number (EAN) Calculation**:
- EAN is calculated as the total number of electrons around the metal ion.
- For \( K_4[Fe(CN)_6] \) (Fe in +2):
- Iron has 26 electrons, and with a +2 oxidation state, it has \( 26 - 2 = 24 \) electrons.
- Each \( CN^- \) donates 2 electrons, and with 6 ligands, the total contribution is \( 6 \times 2 = 12 \).
- Therefore, EAN = \( 24 + 12 = 36 \).

- For \( K_3[Fe(CN)_6] \) (Fe in +3):
- Iron has 26 electrons, and with a +3 oxidation state, it has \( 26 - 3 = 23 \) electrons.
- The contribution from the ligands remains the same, \( 12 \).
- Therefore, EAN = \( 23 + 12 = 35 \).

5. **Conclusion**:
- The assertion that \( K_4[Fe(CN)_6] \) is less stable than \( K_3[Fe(CN)_6] \) is correct.
- The reason provided (EAN of Fe in \( K_4[Fe(CN)_6] \) is 36) is also correct, but it does not explain the stability difference adequately since EAN is more relevant for carbonyl compounds than for cyanide complexes.

### Final Answer:
- The assertion is true, and the reason is true but does not explain the assertion.